About
Cześć! I am a second yeah PhD Student at University of California Los Angeles (UCLA). I'm a part of the probability research group working with professors Georg Menz and Marek Biskup. My research interest lie in Interacting Particle Systems/Glauber Dynamics. See below what fun they are!
Ising controls
Model
Glauber Dynamics of the classical Ising Model on big rectangle \(\Lambda \subset \Z^2\) with parameters \(\beta\), \(J\geq 0\), \(h\in\R\). Each time-step a configuration \(\sigma\in\{-1,1\}^{\Lambda}\) is updated by the following rule: Choose a site \(i\in\Lambda\) uniformly. With probability \(\min\{1,e^{-2\beta\sigma_i(h + J\sum_{j\sim i}\sigma_j)}\}\) the sign of \(\sigma_i\) is flipped. On a finite lattice the process converges almost surely to the Ising model, i.e. a measure given by \(\mu(\{\sigma\})=\frac{e^{-\beta H(\sigma)}}{Z}\), where \(H(\sigma) = -J\sum_{i\sim j}\sigma_i\sigma_j -h\sum_{i}\sigma_i\) and \(Z\) is chosen so that this is a probability measure.